I am trying to develop a general relationship for the velocity needed to purge an air bubble from a water system with multiple high spots. Any suggestions.
Yes, a suggestion. Not that I've tried this, mind you.
Anyway, assume the bubble is a sphere. And assume a bubble size. You can find graphs for the drag coefficient of a sphere. Then calculate the drag, set the drag force times the sine of the slope angle equal to the buoyant force acting up on the bubble and see what you get.
This would be approximate for several reasons. Even if the bubble were sphere-shaped, it wouldn't have the same boundary conditions at the fluid surface as a solid. And a sphere against a wall would be in reduced fluid velocity and would be even less sphere-shaped. But it's a start.
The alternative is either do testing or find someone that has.